A phylogenetic tree is a visual diagram of the relationship between a set of biological species. The scientists usually use it to analyze many characteristics of the species. The distance-matrix methods, such as Unweighted Pair Group Method with Arithmetic Mean and Neighbor Joining, construct a phylogenetic tree by calculating pairwise genetic distances between taxa. These methods have the computational performance issue. Although several new methods with high-performance hardware and frameworks have been proposed, the issue still exists. In this work, a novel parallel Unweighted Pair Group Method with Arithmetic Mean approach on multiple Graphics Processing Units is proposed to construct a phylogenetic tree from extremely large set of sequences. The experimental results present that the proposed approach on a DGX-1 server with 8 NVIDIA P100 graphic cards achieves approximately 3-fold to 7-fold speedup over the implementation of Unweighted Pair Group Method with Arithmetic Mean on a modern CPU and a single GPU, respectively.